Homework Help:
Stat Physics (Equilibrium)

1. The problem statement, all variables and given/known data
A box is separated by a partition which divides its volume in the ratio 3:1. The larger portion of the box contains 1000 molecules of Neon gas, the smaller box contains 100 molecules of Helium gas. A small hole is made in the partition, and one waits until equilibrium is attained.

i) Find the mean number of molecules of each type on either side of the partition.
ii) What is the probability of finding 1000 molecules of of Neon gas in the larger portion and 100 molecules of Helium gas in the smaller (i.e. the same distribution as in the initial system) ?

2. Relevant equations

Pi = [tex]\Omega[/tex]i/[tex]\Omega[/tex]f

where,
[tex]\Omega[/tex]i = initial number of accessible state
[tex]\Omega[/tex]f = final number of accessible state

3. The attempt at a solution
I used the idea of equilibrium, reversible and irreversible processes.

Since the partition exists with a ratio 3:1
Probability of finding N Neon gas in the larger portion = (1/3)N
where,
(1/3) is the probability of finding 1 molecule of Neon gas in the larger portion
N = 1000